{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  预测中国股票市场收益率"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  理论论述 Theory Motivation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我选择的指标是：国内生产总值GDP累计同比增长率\n",
    "\n",
    "选择原因：\n",
    "\n",
    "首先，国内生产总值GDP累计同比增长率通常被视为宏观经济健康状况的指标，反映了整体经济的活跃程度和增长潜力。较高的GDP增速意味着国内企业的生产活动、消费需求和出口都在增加，这通常提升企业的盈利能力，并通过提高股价来反映在股票市场中。因此，GDP增长越强，企业盈利预期越高，从而对股市形成正面支撑。\n",
    "\n",
    "其次，GDP增长往往影响投资者的信心和风险偏好。当GDP增速较高时，投资者对未来经济前景的信心提升，更倾向于投入股市，这推动市场回报率的提升。反之，GDP增长放缓可能导致经济衰退的担忧，引发股市回调。此外，GDP增速较高还可能吸引外资流入中国市场，进一步提升股市需求和流动性。\n",
    "\n",
    "最后，GDP累计同比增长率有助于平滑短期波动，使其能够更好地反映中长期的经济趋势。对于投资者而言，累积数据能提供一个长期稳定的视角，减少单一季度经济数据的波动性和政策变动对股市的短期干扰，从而提升预测股票市场回报率的有效性。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy.stats as stats #统计模块\n",
    "import scipy\n",
    "# import pymysql #导入数据库模块\n",
    "\n",
    "from datetime import datetime #时间模块\n",
    "import statsmodels.formula.api as smf # OLS regression\n",
    "\n",
    "# import pyreadr # read RDS file\n",
    "\n",
    "from matplotlib import style\n",
    "import matplotlib.pyplot as plt #画图模块\n",
    "import matplotlib.dates as mdates\n",
    "\n",
    "from matplotlib.font_manager import FontProperties #作图中文\n",
    "from pylab import mpl\n",
    "\n",
    "# 输出矢量图 渲染矢量图\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format='svg'\n",
    "\n",
    "from IPython.core.interactiveshell import InteractiveShell #jupyter运行输出的模块\n",
    "#显示每一个运行结果\n",
    "InteractiveShell.ast_node_interactivity='all'\n",
    "\n",
    "#设置列不限制数量\n",
    "pd.set_option('display.max_columns',None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  中国股票市场收益率（月度）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Preclose</th>\n",
       "      <th>Open</th>\n",
       "      <th>Highest</th>\n",
       "      <th>Lowest</th>\n",
       "      <th>Close</th>\n",
       "      <th>Volume</th>\n",
       "      <th>Money</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1990-12-19</th>\n",
       "      <td></td>\n",
       "      <td>96.050</td>\n",
       "      <td>99.980</td>\n",
       "      <td>95.790</td>\n",
       "      <td>99.980</td>\n",
       "      <td>126000.00</td>\n",
       "      <td>4.940000e+05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-12-20</th>\n",
       "      <td>99.98</td>\n",
       "      <td>104.300</td>\n",
       "      <td>104.390</td>\n",
       "      <td>99.980</td>\n",
       "      <td>104.390</td>\n",
       "      <td>19700.00</td>\n",
       "      <td>8.400000e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-12-21</th>\n",
       "      <td>104.39</td>\n",
       "      <td>109.070</td>\n",
       "      <td>109.130</td>\n",
       "      <td>103.730</td>\n",
       "      <td>109.130</td>\n",
       "      <td>2800.00</td>\n",
       "      <td>1.600000e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-12-24</th>\n",
       "      <td>109.13</td>\n",
       "      <td>113.570</td>\n",
       "      <td>114.550</td>\n",
       "      <td>109.130</td>\n",
       "      <td>114.550</td>\n",
       "      <td>3200.00</td>\n",
       "      <td>3.100000e+04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-12-25</th>\n",
       "      <td>114.55</td>\n",
       "      <td>120.090</td>\n",
       "      <td>120.250</td>\n",
       "      <td>114.550</td>\n",
       "      <td>120.250</td>\n",
       "      <td>1500.00</td>\n",
       "      <td>6.000000e+03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-24</th>\n",
       "      <td>2748.918</td>\n",
       "      <td>2770.754</td>\n",
       "      <td>2863.152</td>\n",
       "      <td>2761.372</td>\n",
       "      <td>2863.126</td>\n",
       "      <td>4776195.45</td>\n",
       "      <td>4.427953e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-25</th>\n",
       "      <td>2863.126</td>\n",
       "      <td>2901.419</td>\n",
       "      <td>2952.451</td>\n",
       "      <td>2889.048</td>\n",
       "      <td>2896.306</td>\n",
       "      <td>5682598.16</td>\n",
       "      <td>5.166981e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-26</th>\n",
       "      <td>2896.306</td>\n",
       "      <td>2893.745</td>\n",
       "      <td>3000.953</td>\n",
       "      <td>2889.014</td>\n",
       "      <td>3000.953</td>\n",
       "      <td>5763192.61</td>\n",
       "      <td>5.246691e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-27</th>\n",
       "      <td>3000.953</td>\n",
       "      <td>3049.103</td>\n",
       "      <td>3087.529</td>\n",
       "      <td>3017.445</td>\n",
       "      <td>3087.529</td>\n",
       "      <td>4922871.63</td>\n",
       "      <td>4.806126e+07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>3087.529</td>\n",
       "      <td>3194.722</td>\n",
       "      <td>3358.588</td>\n",
       "      <td>3153.697</td>\n",
       "      <td>3336.497</td>\n",
       "      <td>11023379.17</td>\n",
       "      <td>1.167773e+08</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8251 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Preclose      Open   Highest    Lowest     Close       Volume  \\\n",
       "Day                                                                         \n",
       "1990-12-19              96.050    99.980    95.790    99.980    126000.00   \n",
       "1990-12-20     99.98   104.300   104.390    99.980   104.390     19700.00   \n",
       "1990-12-21    104.39   109.070   109.130   103.730   109.130      2800.00   \n",
       "1990-12-24    109.13   113.570   114.550   109.130   114.550      3200.00   \n",
       "1990-12-25    114.55   120.090   120.250   114.550   120.250      1500.00   \n",
       "...              ...       ...       ...       ...       ...          ...   \n",
       "2024-09-24  2748.918  2770.754  2863.152  2761.372  2863.126   4776195.45   \n",
       "2024-09-25  2863.126  2901.419  2952.451  2889.048  2896.306   5682598.16   \n",
       "2024-09-26  2896.306  2893.745  3000.953  2889.014  3000.953   5763192.61   \n",
       "2024-09-27  3000.953  3049.103  3087.529  3017.445  3087.529   4922871.63   \n",
       "2024-09-30  3087.529  3194.722  3358.588  3153.697  3336.497  11023379.17   \n",
       "\n",
       "                   Money  \n",
       "Day                       \n",
       "1990-12-19  4.940000e+05  \n",
       "1990-12-20  8.400000e+04  \n",
       "1990-12-21  1.600000e+04  \n",
       "1990-12-24  3.100000e+04  \n",
       "1990-12-25  6.000000e+03  \n",
       "...                  ...  \n",
       "2024-09-24  4.427953e+07  \n",
       "2024-09-25  5.166981e+07  \n",
       "2024-09-26  5.246691e+07  \n",
       "2024-09-27  4.806126e+07  \n",
       "2024-09-30  1.167773e+08  \n",
       "\n",
       "[8251 rows x 7 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv(\"D:/python-homework/python-homework/000001.csv\")#导入数据\n",
    "data['Day']=pd.to_datetime(data['Day'],format='%Y/%m/%d')#变成时间格式\n",
    "data.set_index('Day',inplace=True)#生成索引\n",
    "data.sort_values(by=['Day'],axis=0,ascending=True)#升序排序"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Preclose</th>\n",
       "      <th>Open</th>\n",
       "      <th>Highest</th>\n",
       "      <th>Lowest</th>\n",
       "      <th>Close</th>\n",
       "      <th>Volume</th>\n",
       "      <th>Money</th>\n",
       "      <th>Raw_return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-01-03</th>\n",
       "      <td>647.870</td>\n",
       "      <td>637.720</td>\n",
       "      <td>647.710</td>\n",
       "      <td>630.530</td>\n",
       "      <td>639.880</td>\n",
       "      <td>23451800.00</td>\n",
       "      <td>1.806930e+08</td>\n",
       "      <td>-0.012333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-04</th>\n",
       "      <td>639.880</td>\n",
       "      <td>641.900</td>\n",
       "      <td>655.510</td>\n",
       "      <td>638.860</td>\n",
       "      <td>653.810</td>\n",
       "      <td>42222000.00</td>\n",
       "      <td>3.069230e+08</td>\n",
       "      <td>0.021770</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-05</th>\n",
       "      <td>653.810</td>\n",
       "      <td>655.380</td>\n",
       "      <td>657.520</td>\n",
       "      <td>645.810</td>\n",
       "      <td>646.890</td>\n",
       "      <td>43012300.00</td>\n",
       "      <td>3.015330e+08</td>\n",
       "      <td>-0.010584</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-06</th>\n",
       "      <td>646.890</td>\n",
       "      <td>642.750</td>\n",
       "      <td>643.890</td>\n",
       "      <td>636.330</td>\n",
       "      <td>640.760</td>\n",
       "      <td>48748200.00</td>\n",
       "      <td>3.537580e+08</td>\n",
       "      <td>-0.009476</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-01-09</th>\n",
       "      <td>640.760</td>\n",
       "      <td>637.520</td>\n",
       "      <td>637.550</td>\n",
       "      <td>625.040</td>\n",
       "      <td>626.000</td>\n",
       "      <td>50985100.00</td>\n",
       "      <td>3.985190e+08</td>\n",
       "      <td>-0.023035</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-24</th>\n",
       "      <td>2748.918</td>\n",
       "      <td>2770.754</td>\n",
       "      <td>2863.152</td>\n",
       "      <td>2761.372</td>\n",
       "      <td>2863.126</td>\n",
       "      <td>4776195.45</td>\n",
       "      <td>4.427953e+07</td>\n",
       "      <td>0.041547</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-25</th>\n",
       "      <td>2863.126</td>\n",
       "      <td>2901.419</td>\n",
       "      <td>2952.451</td>\n",
       "      <td>2889.048</td>\n",
       "      <td>2896.306</td>\n",
       "      <td>5682598.16</td>\n",
       "      <td>5.166981e+07</td>\n",
       "      <td>0.011589</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-26</th>\n",
       "      <td>2896.306</td>\n",
       "      <td>2893.745</td>\n",
       "      <td>3000.953</td>\n",
       "      <td>2889.014</td>\n",
       "      <td>3000.953</td>\n",
       "      <td>5763192.61</td>\n",
       "      <td>5.246691e+07</td>\n",
       "      <td>0.036131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-27</th>\n",
       "      <td>3000.953</td>\n",
       "      <td>3049.103</td>\n",
       "      <td>3087.529</td>\n",
       "      <td>3017.445</td>\n",
       "      <td>3087.529</td>\n",
       "      <td>4922871.63</td>\n",
       "      <td>4.806126e+07</td>\n",
       "      <td>0.028850</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>3087.529</td>\n",
       "      <td>3194.722</td>\n",
       "      <td>3358.588</td>\n",
       "      <td>3153.697</td>\n",
       "      <td>3336.497</td>\n",
       "      <td>11023379.17</td>\n",
       "      <td>1.167773e+08</td>\n",
       "      <td>0.080637</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>7223 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Preclose      Open   Highest    Lowest     Close       Volume  \\\n",
       "Day                                                                         \n",
       "1995-01-03   647.870   637.720   647.710   630.530   639.880  23451800.00   \n",
       "1995-01-04   639.880   641.900   655.510   638.860   653.810  42222000.00   \n",
       "1995-01-05   653.810   655.380   657.520   645.810   646.890  43012300.00   \n",
       "1995-01-06   646.890   642.750   643.890   636.330   640.760  48748200.00   \n",
       "1995-01-09   640.760   637.520   637.550   625.040   626.000  50985100.00   \n",
       "...              ...       ...       ...       ...       ...          ...   \n",
       "2024-09-24  2748.918  2770.754  2863.152  2761.372  2863.126   4776195.45   \n",
       "2024-09-25  2863.126  2901.419  2952.451  2889.048  2896.306   5682598.16   \n",
       "2024-09-26  2896.306  2893.745  3000.953  2889.014  3000.953   5763192.61   \n",
       "2024-09-27  3000.953  3049.103  3087.529  3017.445  3087.529   4922871.63   \n",
       "2024-09-30  3087.529  3194.722  3358.588  3153.697  3336.497  11023379.17   \n",
       "\n",
       "                   Money  Raw_return  \n",
       "Day                                   \n",
       "1995-01-03  1.806930e+08   -0.012333  \n",
       "1995-01-04  3.069230e+08    0.021770  \n",
       "1995-01-05  3.015330e+08   -0.010584  \n",
       "1995-01-06  3.537580e+08   -0.009476  \n",
       "1995-01-09  3.985190e+08   -0.023035  \n",
       "...                  ...         ...  \n",
       "2024-09-24  4.427953e+07    0.041547  \n",
       "2024-09-25  5.166981e+07    0.011589  \n",
       "2024-09-26  5.246691e+07    0.036131  \n",
       "2024-09-27  4.806126e+07    0.028850  \n",
       "2024-09-30  1.167773e+08    0.080637  \n",
       "\n",
       "[7223 rows x 8 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_new=data['1995-01':'2024-09'].copy()#用copy来进行深度复制\n",
    "data_new['Close']=pd.to_numeric(data_new['Close'])#变成数值型\n",
    "data_new['Preclose']=pd.to_numeric(data_new['Preclose'])#变成数值型\n",
    "#计算回报率\n",
    "data_new['Raw_return']=data_new['Close']/data_new['Preclose']-1\n",
    "data_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Raw_return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Day</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-01-31</th>\n",
       "      <td>-0.131631</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-02-28</th>\n",
       "      <td>-0.023694</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-03-31</th>\n",
       "      <td>0.177803</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-04-30</th>\n",
       "      <td>-0.103552</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-05-31</th>\n",
       "      <td>0.207922</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-05-31</th>\n",
       "      <td>-0.005801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>-0.038684</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-07-31</th>\n",
       "      <td>-0.009656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>-0.032849</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.173908</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>357 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Raw_return\n",
       "Day                   \n",
       "1995-01-31   -0.131631\n",
       "1995-02-28   -0.023694\n",
       "1995-03-31    0.177803\n",
       "1995-04-30   -0.103552\n",
       "1995-05-31    0.207922\n",
       "...                ...\n",
       "2024-05-31   -0.005801\n",
       "2024-06-30   -0.038684\n",
       "2024-07-31   -0.009656\n",
       "2024-08-31   -0.032849\n",
       "2024-09-30    0.173908\n",
       "\n",
       "[357 rows x 1 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#计算出月度收益率\n",
    "Month_data=data_new.resample('ME')['Raw_return'].apply(lambda x:(1+x).prod()-1).to_frame()\n",
    "Month_data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  预测变量：国内生产总值GDP累计同比增长率"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 此处需删去缺失值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>rate</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>date</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1991-12-31</th>\n",
       "      <td>9.2628</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1992-03-31</th>\n",
       "      <td>13.6000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1992-06-30</th>\n",
       "      <td>13.8000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1992-09-30</th>\n",
       "      <td>14.1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1992-12-31</th>\n",
       "      <td>14.3000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-06-30</th>\n",
       "      <td>5.5000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-09-30</th>\n",
       "      <td>5.2000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-12-31</th>\n",
       "      <td>5.2000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-03-31</th>\n",
       "      <td>5.3000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>5.0000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>131 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "               rate\n",
       "date               \n",
       "1991-12-31   9.2628\n",
       "1992-03-31  13.6000\n",
       "1992-06-30  13.8000\n",
       "1992-09-30  14.1000\n",
       "1992-12-31  14.3000\n",
       "...             ...\n",
       "2023-06-30   5.5000\n",
       "2023-09-30   5.2000\n",
       "2023-12-31   5.2000\n",
       "2024-03-31   5.3000\n",
       "2024-06-30   5.0000\n",
       "\n",
       "[131 rows x 1 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inflation=pd.read_csv(\"D:/python-homework/python-homework/国内生产总值GDP累计同比.csv\")\n",
    "inflation.dropna(axis=0, how='any', inplace=True)#删去缺失值\n",
    "inflation['date']=pd.to_datetime(inflation['date'],format='%Y-%m-%d')#变成时间格式\n",
    "inflation.set_index('date',inplace=True)#设置成索引\n",
    "inflation.sort_values(by=['date'],axis=0,ascending=True)#升序排序\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  股票市场的风险"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>RV</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>month</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-01-31</th>\n",
       "      <td>0.005695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-02-28</th>\n",
       "      <td>0.018086</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-03-31</th>\n",
       "      <td>0.013378</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-04-30</th>\n",
       "      <td>0.008281</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-05-31</th>\n",
       "      <td>0.148387</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-05-31</th>\n",
       "      <td>0.000915</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>0.000642</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-07-31</th>\n",
       "      <td>0.001441</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>0.000705</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.011045</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>357 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                  RV\n",
       "month               \n",
       "1995-01-31  0.005695\n",
       "1995-02-28  0.018086\n",
       "1995-03-31  0.013378\n",
       "1995-04-30  0.008281\n",
       "1995-05-31  0.148387\n",
       "...              ...\n",
       "2024-05-31  0.000915\n",
       "2024-06-30  0.000642\n",
       "2024-07-31  0.001441\n",
       "2024-08-31  0.000705\n",
       "2024-09-30  0.011045\n",
       "\n",
       "[357 rows x 1 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "market_varince = data_new.resample('ME').apply(\n",
    "    {\n",
    "        'Raw_return':lambda x:sum(x**2)\n",
    "    }\n",
    ")\n",
    "market_varince.reset_index(inplace=True)#把索引给去掉\n",
    "market_varince.rename(columns={'Day':'month','Raw_return':'RV'},inplace=True)#把名字给换掉\n",
    "market_varince.set_index('month',inplace=True)#用月当作索引\n",
    "market_varince"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Raw_return</th>\n",
       "      <th>rate</th>\n",
       "      <th>RV</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1995-03-31</th>\n",
       "      <td>0.177803</td>\n",
       "      <td>11.9</td>\n",
       "      <td>0.013378</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-06-30</th>\n",
       "      <td>-0.099827</td>\n",
       "      <td>11.4</td>\n",
       "      <td>0.009183</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-09-30</th>\n",
       "      <td>-0.001989</td>\n",
       "      <td>11.0</td>\n",
       "      <td>0.004119</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1995-12-31</th>\n",
       "      <td>-0.133902</td>\n",
       "      <td>11.0</td>\n",
       "      <td>0.004399</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1996-03-31</th>\n",
       "      <td>0.006239</td>\n",
       "      <td>10.9</td>\n",
       "      <td>0.011640</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-06-30</th>\n",
       "      <td>-0.000781</td>\n",
       "      <td>5.5</td>\n",
       "      <td>0.000987</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-09-30</th>\n",
       "      <td>-0.003013</td>\n",
       "      <td>5.2</td>\n",
       "      <td>0.000884</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2023-12-31</th>\n",
       "      <td>-0.018067</td>\n",
       "      <td>5.2</td>\n",
       "      <td>0.001009</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-03-31</th>\n",
       "      <td>0.008622</td>\n",
       "      <td>5.3</td>\n",
       "      <td>0.000841</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>-0.038684</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.000642</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>118 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Raw_return  rate        RV\n",
       "1995-03-31    0.177803  11.9  0.013378\n",
       "1995-06-30   -0.099827  11.4  0.009183\n",
       "1995-09-30   -0.001989  11.0  0.004119\n",
       "1995-12-31   -0.133902  11.0  0.004399\n",
       "1996-03-31    0.006239  10.9  0.011640\n",
       "...                ...   ...       ...\n",
       "2023-06-30   -0.000781   5.5  0.000987\n",
       "2023-09-30   -0.003013   5.2  0.000884\n",
       "2023-12-31   -0.018067   5.2  0.001009\n",
       "2024-03-31    0.008622   5.3  0.000841\n",
       "2024-06-30   -0.038684   5.0  0.000642\n",
       "\n",
       "[118 rows x 3 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#通过索引匹配，把三个数据合并\n",
    "reg_data=pd.merge(Month_data,inflation,left_index=True,right_index=True,how='inner')\n",
    "reg_data=pd.merge(reg_data,market_varince,left_index=True,right_index=True,how='inner')\n",
    "reg_data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  描述性统计"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    118.000\n",
       "mean       8.526\n",
       "std        3.220\n",
       "min       -6.900\n",
       "25%        7.000\n",
       "50%        8.600\n",
       "75%       10.500\n",
       "max       18.700\n",
       "Name: rate, dtype: float64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_data['rate'].describe().round(3)#保留3位小数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "共有118个数据，平均值是8.526，标准差是3.22，最大值是18.7，发生在2021年3月，有可能是因为随着疫情防控取得成效，企业复工复产加快，生产活动逐步恢复正常，经济复苏，最小值是-6.9，发生在2020年3月，有可能是因为疫情冲击导致经济活动大规模停滞。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Raw_return    0.896\n",
       "rate         -1.009\n",
       "RV            4.108\n",
       "dtype: float64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Raw_return     2.322\n",
       "rate           4.907\n",
       "RV            24.779\n",
       "dtype: float64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#看峰度和偏度\n",
    "reg_data.skew().round(3)#偏度\n",
    "reg_data.kurt().round(3)#峰度"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "国内生产总值GDP累计同比增长率（季度）是往负偏的，股票市场回报率是往正偏的：\n",
    "\n",
    "股市回报率的峰度（2.322）：这个正峰度值表明股市回报率的分布比正态分布更尖，尾部较重。这意味着股市回报率中包含更多的极端值或离群值，数据集中在平均值附近，但有较大波动的可能性。换句话说，股市回报率可能更容易出现极端涨跌情况，这种分布特征在金融数据中常见，因为市场波动较大，且对外部因素敏感。\n",
    "\n",
    "国内生产总值GDP累计同比增长率的峰度（4.907）：较高的正峰度值（4.907）表明GDP增速的分布具有非常尖锐的峰值和更重的尾部。这意味着GDP增速的值更集中在均值附近，但也存在更显著的极端变化情况。高峰度可能反映出GDP增速在某些特殊时期（如经济危机或快速增长期）出现过剧烈波动。相比股市回报率，GDP增速的极端值更多，这可能源于政策调整、国际环境变化等带来的经济剧烈波动。\n",
    "\n",
    "整体分析： 这种峰度特征显示，尽管两者均有一定极端值的出现，但GDP累计同比增长率的分布更具波动性，集中在平均值附近但波动范围大。股市回报率的峰度较GDP累计同比增长率更低，说明其波动性虽高但不及GDP增速。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  图"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  inflation图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
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   ],
   "source": [
    "fig, ax=plt.subplots(figsize=(14,8))\n",
    "\n",
    "ax.plot(inflation['rate'],label='Inflation',#图片数据\n",
    "linestyle='-',#图片类型，\n",
    "color='#D98719',#图片颜色\n",
    "linewidth=4,#图片线宽\n",
    "marker='o')\n",
    "ax.set_ylabel('Inflation')\n",
    "#添加图例\n",
    "ax.legend(loc='upper right',fontsize=12)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### inflation和Return一起作图（预测变量和收益率图）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 1400x800 with 2 Axes>"
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     "metadata": {},
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   ],
   "source": [
    "# 画多条直线图\n",
    "fig, ax1=plt.subplots(figsize=(14,8))\n",
    "ax1.plot(reg_data['Raw_return'].shift(1),label='Return',\n",
    "linestyle='-',#图片类型，\n",
    "color='red',#图片颜色\n",
    "linewidth=4,#图片线宽\n",
    "marker='o')\n",
    "ax1.set_ylabel('Return',color='red')\n",
    "data_format=mdates.DateFormatter('%Y')\n",
    "ax1.xaxis.set_major_formatter(data_format)\n",
    "ax1.xaxis.set_major_locator(mdates.YearLocator())\n",
    "plt.xticks(rotation=90)\n",
    "ax2=ax1.twinx()#把图纸镜像转一下\n",
    "ax2.plot(reg_data['rate'],label='inflation',\n",
    "linestyle='-',#图片类型，\n",
    "color='blue',#图片颜色\n",
    "linewidth=4,#图片线宽\n",
    "marker='o')\n",
    "ax2.set_ylabel('Inflation',color='blue')\n",
    "\n",
    "plt.title(\"China's Return and Inflation\")\n",
    "#提取图例\n",
    "lines,labels=ax1.get_legend_handles_labels()\n",
    "lines2,labels2=ax2.get_legend_handles_labels()\n",
    "ax2.legend(lines+lines2,labels+labels2,loc='upper right')#合并到第二张图\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## OLS 回归（预测回归）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 模型\n",
    "\n",
    "$$\n",
    "R_t = \\alpha+\\beta*Rate_{t-1}+ \\epsilon_t\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "全样本 Full-Sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                     RV   R-squared:                       0.057\n",
      "Model:                            OLS   Adj. R-squared:                  0.049\n",
      "Method:                 Least Squares   F-statistic:                     4.880\n",
      "Date:                Sat, 16 Nov 2024   Prob (F-statistic):             0.0291\n",
      "Time:                        14:11:32   Log-Likelihood:                 422.77\n",
      "No. Observations:                 117   AIC:                            -841.5\n",
      "Df Residuals:                     115   BIC:                            -836.0\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0008      0.002      0.489      0.625      -0.002       0.004\n",
      "lrate          0.0005      0.000      2.209      0.027    5.63e-05       0.001\n",
      "==============================================================================\n",
      "Omnibus:                      139.938   Durbin-Watson:                   1.484\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):             3632.931\n",
      "Skew:                           4.208   Prob(JB):                         0.00\n",
      "Kurtosis:                      28.969   Cond. No.                         26.3\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 6 lags and without small sample correction\n"
     ]
    }
   ],
   "source": [
    "reg_data['lRV'] = reg_data['RV'].shift(1)\n",
    "reg_data['lrate']=reg_data['rate'].shift(1)#有滞后性\n",
    "model_forecast_rv = smf.ols('RV ~ lrate', data=reg_data).fit(\n",
    "    cov_type='HAC' ,\n",
    "    cov_kwds={'maxlags':6}\n",
    ")   #左边的是被解释变量，右边的是解释变量\n",
    "print(model_forecast_rv.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Adjusted R-squared为4.9%,显著\n",
    "\n",
    "正相关\n",
    "\n",
    "回归显示用该指标预测犯错的概率很小（p值很小）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "子样本 Sub-Sample"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "缩短样本的长度，选取2010年以后的数据，看看结果会不会好一点"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                     RV   R-squared:                       0.074\n",
      "Model:                            OLS   Adj. R-squared:                  0.064\n",
      "Method:                 Least Squares   F-statistic:                     3.002\n",
      "Date:                Sat, 16 Nov 2024   Prob (F-statistic):             0.0864\n",
      "Time:                        14:11:35   Log-Likelihood:                 390.28\n",
      "No. Observations:                  98   AIC:                            -776.6\n",
      "Df Residuals:                      96   BIC:                            -771.4\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0010      0.002      0.679      0.497      -0.002       0.004\n",
      "lrate          0.0004      0.000      1.733      0.083   -4.88e-05       0.001\n",
      "==============================================================================\n",
      "Omnibus:                       64.415   Durbin-Watson:                   1.185\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              244.696\n",
      "Skew:                           2.326   Prob(JB):                     7.33e-54\n",
      "Kurtosis:                       9.187   Cond. No.                         24.2\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 6 lags and without small sample correction\n"
     ]
    }
   ],
   "source": [
    "reg_data['lRV'] = reg_data['RV'].shift(1)\n",
    "reg_data['lrate']=reg_data['rate'].shift(1)\n",
    "model_forecast_rv = smf.ols('RV ~ lrate', data=reg_data['2000':]).fit(\n",
    "    cov_type='HAC' ,\n",
    "    cov_kwds={'maxlags':6}\n",
    ")  \n",
    "print(model_forecast_rv.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Adjusted R-squared为6.4%，显著，模型解释力大\n",
    "\n",
    "正相关\n",
    "\n",
    "回归显示用该指标预测犯错的概率仍比较小，p值大于0.05但小于0.1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                     RV   R-squared:                       0.201\n",
      "Model:                            OLS   Adj. R-squared:                  0.192\n",
      "Method:                 Least Squares   F-statistic:                     9.510\n",
      "Date:                Sat, 16 Nov 2024   Prob (F-statistic):            0.00267\n",
      "Time:                        14:11:39   Log-Likelihood:                 397.52\n",
      "No. Observations:                  98   AIC:                            -791.0\n",
      "Df Residuals:                      96   BIC:                            -785.9\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0023      0.001      3.886      0.000       0.001       0.003\n",
      "lRV            0.4487      0.146      3.084      0.002       0.164       0.734\n",
      "==============================================================================\n",
      "Omnibus:                       56.113   Durbin-Watson:                   2.185\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              169.041\n",
      "Skew:                           2.097   Prob(JB):                     1.96e-37\n",
      "Kurtosis:                       7.879   Cond. No.                         214.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 6 lags and without small sample correction\n"
     ]
    }
   ],
   "source": [
    "reg_data['lRV'] = reg_data['RV'].shift(1)\n",
    "model_forecast_rv = smf.ols('RV ~ lRV', data=reg_data['2000':]).fit(\n",
    "    cov_type='HAC' ,\n",
    "    cov_kwds={'maxlags':6}\n",
    ")\n",
    "print(model_forecast_rv.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "结果显示这个模型关系非常强，而且p值很小，犯错的概率很小，几乎等于0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                     RV   R-squared:                       0.236\n",
      "Model:                            OLS   Adj. R-squared:                  0.220\n",
      "Method:                 Least Squares   F-statistic:                     5.655\n",
      "Date:                Sat, 16 Nov 2024   Prob (F-statistic):            0.00478\n",
      "Time:                        14:11:46   Log-Likelihood:                 399.74\n",
      "No. Observations:                  98   AIC:                            -793.5\n",
      "Df Residuals:                      95   BIC:                            -785.7\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0002      0.001      0.196      0.845      -0.002       0.002\n",
      "lRV            0.4116      0.130      3.156      0.002       0.156       0.667\n",
      "lrate          0.0003      0.000      2.016      0.044    7.27e-06       0.001\n",
      "==============================================================================\n",
      "Omnibus:                       55.220   Durbin-Watson:                   2.184\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):              173.330\n",
      "Skew:                           2.024   Prob(JB):                     2.30e-38\n",
      "Kurtosis:                       8.104   Cond. No.                     1.98e+03\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 6 lags and without small sample correction\n",
      "[2] The condition number is large, 1.98e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "model_forecast_rv = smf.ols('RV ~ lRV+lrate', data=reg_data['2000':]).fit(\n",
    "    cov_type='HAC' ,\n",
    "    cov_kwds={'maxlags':6}\n",
    ")\n",
    "print(model_forecast_rv.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们可以惊喜地发现，将lRV和lrate融合后模型的解释力变强了，虽然只是加了3%，而且lrate的p值变小了很多，犯错的概率小了很多"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  用加了国内生产总值GDP累计同比增长率的风险RV来预测回报率"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:             Raw_return   R-squared:                       0.001\n",
      "Model:                            OLS   Adj. R-squared:                 -0.010\n",
      "Method:                 Least Squares   F-statistic:                   0.07595\n",
      "Date:                Sat, 16 Nov 2024   Prob (F-statistic):              0.783\n",
      "Time:                        14:11:49   Log-Likelihood:                 118.47\n",
      "No. Observations:                  98   AIC:                            -232.9\n",
      "Df Residuals:                      96   BIC:                            -227.8\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0058      0.011      0.519      0.604      -0.016       0.028\n",
      "fitted_RV     -0.7754      2.814     -0.276      0.783      -6.290       4.739\n",
      "==============================================================================\n",
      "Omnibus:                       13.106   Durbin-Watson:                   1.544\n",
      "Prob(Omnibus):                  0.001   Jarque-Bera (JB):               23.026\n",
      "Skew:                           0.521   Prob(JB):                     1.00e-05\n",
      "Kurtosis:                       5.133   Cond. No.                         439.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 6 lags and without small sample correction\n"
     ]
    }
   ],
   "source": [
    "reg_data_new=reg_data['2000':].copy()\n",
    "reg_data_new['fitted_RV']=model_forecast_rv.fittedvalues\n",
    "\n",
    "model_forecast_return=smf.ols('Raw_return~fitted_RV',data=reg_data_new).fit(\n",
    "    cov_type='HAC' ,\n",
    "    cov_kwds={'maxlags':6}\n",
    ")\n",
    "print(model_forecast_return.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "结果显示加上国内生产总值GDP累计同比增长率以后用股票风险RV预测回报率的解释力不能满意，且犯错的概率很大（p值很大）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:             Raw_return   R-squared:                       0.001\n",
      "Model:                            OLS   Adj. R-squared:                 -0.010\n",
      "Method:                 Least Squares   F-statistic:                   0.08252\n",
      "Date:                Sat, 16 Nov 2024   Prob (F-statistic):              0.775\n",
      "Time:                        14:11:52   Log-Likelihood:                 118.48\n",
      "No. Observations:                  98   AIC:                            -233.0\n",
      "Df Residuals:                      96   BIC:                            -227.8\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept      0.0077      0.015      0.505      0.614      -0.022       0.037\n",
      "lrate         -0.0006      0.002     -0.287      0.774      -0.005       0.004\n",
      "==============================================================================\n",
      "Omnibus:                       13.547   Durbin-Watson:                   1.539\n",
      "Prob(Omnibus):                  0.001   Jarque-Bera (JB):               24.398\n",
      "Skew:                           0.531   Prob(JB):                     5.04e-06\n",
      "Kurtosis:                       5.201   Cond. No.                         24.2\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 6 lags and without small sample correction\n"
     ]
    }
   ],
   "source": [
    "model_rate=smf.ols('Raw_return~lrate',data=reg_data['2000':]).fit(\n",
    "    cov_type='HAC' ,\n",
    "    cov_kwds={'maxlags':6}\n",
    ")\n",
    "print(model_rate.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Adjusted R-squared的值为负数，即该指标对预测不起作用，甚至起反作用。\n",
    "\n",
    "且犯错的概率很大（p值很大）\n",
    "\n",
    "结果显示：国内生产总值GDP累计同比增长率不可以直接预测股票市场回报率。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  市场择时 Market Timing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "由于选择的指标不能用来预测中国股票市场回报率，所以这一部分省略。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  整理结果"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "结果：所选择的国内生产总值GDP累计同比增长率这一指标不能用来预测中国股票市场回报率，但通过回归模型发现该指标与股票市场风险有极高的相关性，且与股票市场风险结合可以使对股票风险模型的解释力变得更强，但国内生产总值GDP累计同比增长率和股票市场风险两者均不能直接用来预测中国股票市场回报率。\n",
    "\n",
    "下面分析该指标预测结果与理论论述不同的可能原因：\n",
    "\n",
    "首先，GDP同比增长率是一个宏观经济指标，通常反映整体经济趋势，而非直接反映市场情绪或投资者行为，难以精确捕捉股市短期波动。股市回报率往往受到市场流动性、投资者预期、货币政策等多种因素的影响，而GDP增长更多反映的是中长期经济表现，二者可能存在时滞效应，影响预测精度。\n",
    "\n",
    "其次，中国的资本市场受政策因素和全球经济环境的影响较大，而GDP增长率难以单独反映这些外部因素。例如，中国市场受到政策指引（如“房住不炒”等政策）、资本管制以及美联储政策的波动影响，GDP增速难以全面捕捉这些变化。\n",
    "\n",
    "最后，GDP同比增长率数据频率较低，季度数据可能无法满足股市的高频波动需求。季度数据的滞后性使其难以迅速响应市场的短期波动。此外，市场还会“预先定价”对经济增长的预期，导致实际GDP发布后对市场的影响减弱。\n",
    "\n",
    "因此，国内生产总值GDP累计同比增长率作为单一指标难以捕捉中国股票市场回报的复杂性，需结合其他宏观及市场情绪指标以提升预测准确性。\n"
   ]
  }
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